# Generalizations of Prime Ideals of Semirings

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Let R be a ring with center Z(R), Î±, Î² be endomorphisms of R. In the present paper we investigate some properties of permuting generalized (Î±, Î²)-n-derivation G of a prime or semiprime ring R associated with a permuting (Î±, Î²)-n-derivation D of R. Among some other results, we...

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The additive reduct of a band semiring is a regular band.

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Let R be a commutative semiring. The purpose of this note is to investigate the concept of 2-absorbing (resp., weakly 2-absorbing) primary ideals generalizing of 2- absorbing (resp., weakly 2-absorbing) ideals of semirings. A proper ideal I of R said to be a 2-absorbing (resp., weakly...

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Let R be an associative ring, Î» a nonzero left ideal of R, d : R â†’ R a derivation and G : R â†’ R a generalized derivation. In this paper, we study the following situations in prime and semiprime rings: (1) G (x o y) = a(xy Â± yx); (2) G[x, y] = a(xy Â± yx); (3) d(x) o d(y) =...

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Given a very strong multiplication semimidule M over a commutative semiring R, a Zariski topology is defined on the spectrum Speck(M) of prime k-subsemimodules of M. The properties and possible structures of this topology are studied.

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We introduce the notion of exact sequence of semimodules over semirings using maximal homomorphisms and generalize some results of module theory to semimodules over semirings. Indeed, we prove, "If 0 â†’ Lf â†’ Mg â†’ N â†’ 0 is a split exact sequence of R-semimodules and...

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In this paper, we consider the weakly special radical classes and special radical classes of ternary semirings. Some of our results are similar to those in rings theory as well as in semiring theory. In particular, the upper radicals of the above two classes are determined.

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Let R be a commutative ring with nonzero identity and let M be an R-module with X = Spec (M). It is introduced a scheme OX on the prime spectrum of M and some of its properties have been investigated.

- Modules Whose Certain Submodules Are Prime. Behboodi, M.; Karamzadeh, O. A. S.; Koohy, H. // Vietnam Journal of Mathematics;Sep2004, Vol. 32 Issue 3, p303
Modules in which every proper submodule (resp. proper nonzero submodule) is prime (called fully prime (almost fully prime)) and with some other related notions are fully investigated. It is shown that over a commutative ring R, an R-module M is fully prime (fully semiprime) if and only if M is a...